Do emulators not let computers work like regular computers or are they just another piece of software?

Emulators are a software emulating another computer. For example, an NES emulator is a software that is ran on a desktop PC to look like the NES (Nintendo Entertainment System), whereas you can play NES titles (Cartridges emulated as ROMs) using your keyboard or a controller for the NES controller.

However, emulators are not just for other computers. Technically, an emulator is a piece of software that allows foreign (different language or setup) hardware or software to interact with the current system. The NES example is a good one. An example with software is like installing windows software on linux. It cannot be done due to language conflicts. An emulator solves this problem.